Saturday's 2-1 home loss to Scunthorpe saw the Iron leapfrog them out of the, leaving the Essex club two points adrift of safety.
"I just need to consider my position now," Dunne told BBC Essex.
"I need to speak to the chairman. He's been very supportive of me. I know what I want to try and do with the club but I love this club too much to see it suffer the way it is at the moment."
Dunne, a former defender who played 167 times across two spells for the U's, will now discuss his future with chairman Robbie Cowling.